What important parts did Dickie Mountbatten and his wife, Edwina, play in the unification of India?

Saurabh Singh
It was "Persuading" more than 500 princely states to join either of to be dominions and most of them being geographically in and around India rather than to be Pakistan, joined India thus giving India the map it has today. As has been pointed by Alex that Mountbatten being representative of British empire -the vanguard of princely states for over a century- and himself being a Royalty, his cajoling carried greater weight coupled with nuanced to open warning of chaos from Sardar Vallabhbhai Patel.

It is even said that Indian national congress accepted June 3 partition plan on tacit understanding that Mountbatten, using his position, will talk sense into princes mind that their independent existence, post withdrawal of British paramountcy, was politically and economically unfeasible and this he (Louis Mountbatten) did most effectively e.g. his July 25 1947 speech to the chamber of princes was tour de force (as pointed by Ramchandra Guha in his "India after Gandhi")

Little Creature
I do not know what part Mountbattens played in unifying India, but their was one person Sardar Vallabhai Patel, who is accredited to be the person behind united India as you all see today.